14949 + Interview Questions in Maths in Class 11 Page 284 InterviewSolution

14151.	What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?
Answer» ANSWER :RS `500 (1.1)^(10)`

Discussion

14152.	(r_(1)-r)(r_(2)-r)(r_(3)-r)=
Answer» 4RR 4Rs `4R DELTA` `4Rr^(2)` ANSWER :D

Discussion

14153.	Find Lt_(xto pi/2)(tan3x)/(tanx)
Answer» ANSWER :`1/3`

Discussion

14154.	The position of a point in time 't' is given by x = 1 + 2t + 3t^(2) and y = 2 - 3t + 4t^(2). Then its acceleration at time 't' is
Answer» 10 12 13 15 Answer :A

Discussion

14155.	If sin beta is the G.M between sin alpha and cos alpha then (cos alpha - sin alpha)^(2) - 2 cos^(2) beta =
Answer» 0 1 2 -1 Answer :D

Discussion

14156.	The side of a triangle are in the ratio 1 : sqrt3 : 2, then the angles of the triangle are in the ratio
Answer» `1 : 3 : 5` `2 : 3 : 4` `3 : 2 : 1` `1 : 2 : 3` ANSWER :D

Discussion

14157.	If the pair of lines ax^(2)+2hxy+by^(2)=0 (h^(2) gt ab) orms an equilateral triangle with the line lr + my + n = 0 then (a+3b)(3a+b)=
Answer» `h^(2)` `2h^(2)` `3h^(2)` `4H^(2)` Answer :D

Discussion

14158.	Through (x_(0), y_(0)) variable line is drawn cut ting the axes at A, B. If OACB is a rectangle then locus of C is
Answer» `(x_(0))/(2X)+(y_(0))/(2y)=1` `(x_(0))/(x)+(y_(0))/(y)=1` `(x_(0))/(3X)+(y_(0))/(3Y)=1` `(2x_(0))/(x)+(2y_(0))/(y)=1` Answer :2

Discussion

14159.	Find the centre and radius of the circle
Answer» SOLUTION :(3/4,-1), `sqrt33/4`

Discussion

14160.	x = log ((1)/(y) + sqrt(1+(1)/(y^(2)))) rArr y=
Answer» TAN H x cot h x sec h x cosec h x Answer :D

Discussion

14161.	If cosx=(-3)/(5),x lies in the third quadrant, find the values of other five trigonometric functions.
Answer» ANSWER :`3/4`

Discussion

14162.	Let U ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {1, 3, 5, 7, 9}. Find A′.
Answer» ANSWER :{2, 4, 6, 8, 10}

Discussion

14163.	Evaluate the following limits : Lim_( x to 0) ( cos mx - cos n x)/(x^(2))
Answer» ANSWER :`(N^(2)-m^(2))/2`

Discussion

14164.	Let a, b and c be distinct non-negative numbers. If the vectors abar(i)+abar(j)+cbar(k), bar(i)+bar(k) and cbar(i)+cbar(j)+b""bar(k) lie in a plane, then c is
Answer» G.M. of a and B A.M. of a and b Equal to zero H.M. of a and b Answer :A

Discussion

14165.	Find the solution of sinx=-(sqrt(3))/(2).
Answer» ANSWER :`x=npi+(-1)^(N)(4pi)/(3),n inZ`

Discussion

14166.	The relation S = {(3,3),(4,4)} on the set A ={2,3,4} is "______".
Answer» an equivalance RELATION REFLEXIVE only not reflexive but SYMMETRIC and TRANSITIVE symmetric only Answer :C

Discussion

14167.	The set of values of 'x' for which (tan3x-tan2x)/(1+tan3xtan2x)=1 is
Answer» only I, II only II, III only I, III I, II, III ANSWER :B

Discussion

14168.	f: R^(+) rarr R is continuous function satisfying f(x/y)=f(x) - f (y) AA x, y in R^(+) . If f'(1) = 1, then
Answer» f is UNBOUNDED `lim_(x rarr0)f(1/x)=0` `lim_(xrarr0)(f(1+x))/x=1` `lim_(x rarr0)x.f(x)=0` ANSWER :A::C::D

Discussion

14169.	If 3tan(theta-15)=tan(theta+15^(0)),0ltthetaltpi then theta =
Answer» `(PI)/(2)` `(pi)/(4)` `(pi)/(6)` `(pi)/(3)` ANSWER :B

Discussion

14170.	If the pair of lines 2x^(2)-5xy+2y^(2)=0 forms a parallelogram with parallel pair which is passing through (3, 3) then its area is
Answer» 1 2 3 4 Answer :C

Discussion

14171.	The probability that a student will pass the final examinatin in both English and Hindi is 0.5 and the probability of pasing neither is 0.1. If the probability of passing the English examination is 0.75. What is the probability of passing the Hindi examination?
Answer» ANSWER :0.65

Discussion

14172.	The range of cot^(-1)(x) is =
Answer» `R` `(0,PI)` `[0,pi]` `(-(pi)/2,(pi)/2)` Answer :B

Discussion

14173.	Solve 2cos^(2)x+3sinx=0.
Answer» ANSWER :`x=npi+(-1)^(N)(7pi)/(6),NINZ`

Discussion

14174.	Find r if""^(5)P_(r)=2""^(6)P_(r-1)
Answer» ANSWER :3

Discussion

14175.	The sum of the series (1)/( log_(2) 4) + (1)/( log_(4) 4) + (1)/( log_(8) 4) + …... + (1)/( log_(2) 4) is
Answer» `(1)/(2) n (n+1) ` `(1)/(12) n ( n+1) (2n+1)` `(1)/( n(n+1) )` ` (n (n+1))/4` ANSWER :D

Discussion

14176.	Find the equation of a straight line in the plane vecr.vecn =d which is parallel to vecr = veca + lamda vecb and passes through the foot of the perpendicular drawn from point P (veca)to vecr.vecn=d(where vecn .vecb=0).
Answer» `VECR= VECA+ ((d- veca.vecn)/( n ^(2))) vecn + lamda VECB` `vecr = veca + ((d - veca.vecn)/(n)) vecn + lamda vecb` `vecr = veca + ((veca. Vecn -d)/(n ^(2))) vecn + lamda vecb ` `vecr = veca + ((veca.vecn-d)/(n)) vecn+lamda vecb` Answer :A

Discussion

14177.	Write downthe slopes of the lines joining P(1, 1) and Q(2, 3)
Answer» ANSWER :2

Discussion

14178.	Solve : tan theta + sec theta = sqrt3.
Answer» ANSWER :`1/2 PI,`

Discussion

14179.	(2 vec(i) + 4vec(j) + 2vec(k)) xx (2vec(i) -p vec(j) + 5vec(k))=16 vec(i) -6vec(j) + 2p vec(k) then p=
Answer» 2 `-2` 0 3 Answer :B

Discussion

14180.	Fill in the blanks to make each of the following a true statement : U′ ∩ A = . . .
Answer» ANSWER :`PHI`

Discussion

14181.	How many integers of four digits each can be formed with the digits 0,1,3,5,6 (assuming no repetitions)
Answer» ANSWER :` 96`

Discussion

14182.	Evaluate the following limits in lim_(xrarr0)((x+1)^(5)-1)/(x)
Answer» ANSWER :5

Discussion

14183.	Differentiate (1)/( x^3) with respect to x from definition.
Answer» ANSWER :`(d)/( DX) ((1)/( x^3) ) = (-3)/( x^4)`

Discussion

14184.	Show that the lines joining the origin to the two points of intersection of the curves ax^(2)+2hxy+by^(2)+2gx=0, a_(1)x^(2)+2h_(1)xy+b_(1)y^(2)+2g_(1)x=0 will be at right angles to one another if g(a_(1)+b_(1))=g_(1)(a+b)
Answer» ANSWER :`g_(1)(a+b)`

Discussion

14185.	Solve 2sin^(2)x+sin^(2)2x=2
Answer» ANSWER :`{npi pm(pi)/(4)} CUP {N pi pm(pi)/(2)}`

Discussion

14186.	A coin and dice are tossed . Then ….. Is the probability that coin shows head and dice shows number 6 .
Answer» ANSWER :`1/12`

Discussion

14187.	(ii) Let y= (x)/(a^(2) +x^(2))then find dy/dx
Answer» ANSWER :`= (a^2 - x^2)/((a^2 + x^2)^2)`.

Discussion

14188.	Find the equation of a parabola whose vertex at (-2,3) and the focus at (1,3).
Answer» ANSWER :`(3x+4y+24)^(2)`

Discussion

14189.	Evaluate (iv) (cos theta - sin theta) if (a)theta = (7 pi)/(4)(b) theta = (11 pi)/(3)
Answer» ANSWER :`(SQRT(3)+1)/(2)`

Discussion

14190.	If x lt 0." then "tan^(-1)x is equal to
Answer» `-PI+"cot"^(-1)1/X` `"sin"^(-1)x/(sqrt(1+x^(2)))` `-"cos"^(-1)1/(sqrt(1+x^(2)))` `-"COSEC"^(-1)(sqrt(1+x^(2)))/x` Answer :A::B::C::D

Discussion

14191.	........is the length of the arc of the circle with radius 28 cm and angle made by two radii at centre is 45^@ .
Answer» ANSWER :22 CM

Discussion

14192.	How many 6 - digit numbers can be formed the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated ?
Answer» ANSWER :120

Discussion

14193.	An experiment consists of lossing a coin and then throwing it second time if a head occurs on the first loss, then a die is rolled once. Find the sample space.
Answer» Answer :{HH, HT, T1, T2, T3, T4, T5, T6}

Discussion

14194.	If f(x) =x^(3) +ax^(2)+bx +5 sin^(2) x is an increasing function on R, then
Answer» `a^(2)-3b-15le0` `a^(2)-3b+15ge0` `a^(2)-3b+15le0` `agt0andblt0` ANSWER :A::C

Discussion

14195.	Evaluate the following limits : Lim_(x to 0) (sin 2x (1- cos 2x))/(x^(3))
Answer» ANSWER :4

Discussion

14196.	In R^(3) equation x^(2)+y^(2)=0 represents ____ .
Answer» ANSWER :Z- AXIS

Discussion

14197.	A coin is tossed.If its shows a tail we draw a ball from a box which contains 2 red and 3 black balls.If it shows head we throw a die.Find the sample space for this experiment
Answer» Answer :`{TR_(1), TR_(2), TB_(1), TB_(2), TB_(3), H1, H2, H3, H4, H5, H6}`

Discussion

14198.	Let ybe an implicit function of x defines by x^(2x) - 2x^x cot y - 1 = 0, then y^1(1) is equal to
Answer» `1` `LN 2` `-ln 2` `-1` ANSWER :D

Discussion

14199.	A regular pentagon and regular decagon have the same perimeter thenthe ratio of their areas is
Answer» `1 : sqrt5` `2 : sqrt5` `3 : sqrt5` `4 : sqrt5` ANSWER :B

Discussion

14200.	Which two consecutive terms in the expansion (1 +x)^(15)have equal coefficients.
Answer» ANSWER :`T_(8)` and `T_(9)`

Discussion

Explore topic-wise InterviewSolutions in .

What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?

(r_(1)-r)(r_(2)-r)(r_(3)-r)=

Find Lt_(xto pi/2)(tan3x)/(tanx)

The position of a point in time 't' is given by x = 1 + 2t + 3t^(2) and y = 2 - 3t + 4t^(2). Then its acceleration at time 't' is

If sin beta is the G.M between sin alpha and cos alpha then (cos alpha - sin alpha)^(2) - 2 cos^(2) beta =

The side of a triangle are in the ratio 1 : sqrt3 : 2, then the angles of the triangle are in the ratio

If the pair of lines ax^(2)+2hxy+by^(2)=0 (h^(2) gt ab) orms an equilateral triangle with the line lr + my + n = 0 then (a+3b)(3a+b)=

Through (x_(0), y_(0)) variable line is drawn cut ting the axes at A, B. If OACB is a rectangle then locus of C is

Find the centre and radius of the circle

x = log ((1)/(y) + sqrt(1+(1)/(y^(2)))) rArr y=

If cosx=(-3)/(5),x lies in the third quadrant, find the values of other five trigonometric functions.

Let U ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {1, 3, 5, 7, 9}. Find A′.

Evaluate the following limits : Lim_( x to 0) ( cos mx - cos n x)/(x^(2))

Let a, b and c be distinct non-negative numbers. If the vectors abar(i)+abar(j)+cbar(k), bar(i)+bar(k) and cbar(i)+cbar(j)+b""bar(k) lie in a plane, then c is

Find the solution of sinx=-(sqrt(3))/(2).

The relation S = {(3,3),(4,4)} on the set A ={2,3,4} is "______".

The set of values of 'x' for which (tan3x-tan2x)/(1+tan3xtan2x)=1 is

f: R^(+) rarr R is continuous function satisfying f(x/y)=f(x) - f (y) AA x, y in R^(+) . If f'(1) = 1, then

If 3tan(theta-15)=tan(theta+15^(0)),0ltthetaltpi then theta =

If the pair of lines 2x^(2)-5xy+2y^(2)=0 forms a parallelogram with parallel pair which is passing through (3, 3) then its area is

The probability that a student will pass the final examinatin in both English and Hindi is 0.5 and the probability of pasing neither is 0.1. If the probability of passing the English examination is 0.75. What is the probability of passing the Hindi examination?

The range of cot^(-1)(x) is =

Solve 2cos^(2)x+3sinx=0.

Find r if""^(5)P_(r)=2""^(6)P_(r-1)

The sum of the series (1)/( log_(2) 4) + (1)/( log_(4) 4) + (1)/( log_(8) 4) + …... + (1)/( log_(2) 4) is

Find the equation of a straight line in the plane vecr.vecn =d which is parallel to vecr = veca + lamda vecb and passes through the foot of the perpendicular drawn from point P (veca)to vecr.vecn=d(where vecn .vecb=0).

Write downthe slopes of the lines joining P(1, 1) and Q(2, 3)

Solve : tan theta + sec theta = sqrt3.

(2 vec(i) + 4vec(j) + 2vec(k)) xx (2vec(i) -p vec(j) + 5vec(k))=16 vec(i) -6vec(j) + 2p vec(k) then p=

Fill in the blanks to make each of the following a true statement : U′ ∩ A = . . .

How many integers of four digits each can be formed with the digits 0,1,3,5,6 (assuming no repetitions)

Evaluate the following limits in lim_(xrarr0)((x+1)^(5)-1)/(x)

Differentiate (1)/( x^3) with respect to x from definition.

Show that the lines joining the origin to the two points of intersection of the curves ax^(2)+2hxy+by^(2)+2gx=0, a_(1)x^(2)+2h_(1)xy+b_(1)y^(2)+2g_(1)x=0 will be at right angles to one another if g(a_(1)+b_(1))=g_(1)(a+b)

Solve 2sin^(2)x+sin^(2)2x=2

A coin and dice are tossed . Then ….. Is the probability that coin shows head and dice shows number 6 .

(ii) Let y= (x)/(a^(2) +x^(2))then find dy/dx

Find the equation of a parabola whose vertex at (-2,3) and the focus at (1,3).

Evaluate (iv) (cos theta - sin theta) if (a)theta = (7 pi)/(4)(b) theta = (11 pi)/(3)

If x lt 0." then "tan^(-1)x is equal to

........is the length of the arc of the circle with radius 28 cm and angle made by two radii at centre is 45^@ .

How many 6 - digit numbers can be formed the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated ?

An experiment consists of lossing a coin and then throwing it second time if a head occurs on the first loss, then a die is rolled once. Find the sample space.

If f(x) =x^(3) +ax^(2)+bx +5 sin^(2) x is an increasing function on R, then

Evaluate the following limits : Lim_(x to 0) (sin 2x (1- cos 2x))/(x^(3))

In R^(3) equation x^(2)+y^(2)=0 represents ____ .

A coin is tossed.If its shows a tail we draw a ball from a box which contains 2 red and 3 black balls.If it shows head we throw a die.Find the sample space for this experiment

Let ybe an implicit function of x defines by x^(2x) - 2x^x cot y - 1 = 0, then y^1(1) is equal to

A regular pentagon and regular decagon have the same perimeter thenthe ratio of their areas is

Which two consecutive terms in the expansion (1 +x)^(15)have equal coefficients.